Metal covered with glass makes the mesh always visible in cycles?
Looks like overlapping geometry to me. What happens when you drag the glas object just a tiny bit upwards? – brockmann


Wow, that did the trick, thanks a lot! I also had to change the ring size so no face are touching anymore, now it looks perfect. Just out of interest - is there a less "hacky" way? Fusing both with a boolean operator didn't help.